(a)[1]
Calculate the value of $p$.
(b)[3]
On the grid, use a scale of $2\text{ cm}$ to $1$ unit to draw a horizontal $x$-axis for $-2 \le x \le 4$, and use a scale of $1\text{ cm}$ to $1$ unit to draw a vertical $y$-axis for $0 \le y \le 10$; then plot the points from the table and join them with a smooth curve.
(c)[2]
Use a tangent line to estimate the gradient of the curve at the point where $x = 2.5$.
(d(i))[1]
On the same grid, draw the straight line passing through $(-0.4, 0)$ and $(2, 3.6)$.
(d(ii))[2]
Find the equation of this line in the form $y = mx + c$.
(d(iii))[1]
State the $x$-coordinates of the points where the line cuts the curve.
(d(iv))[2]
The given $x$-coordinates satisfy $2^x = Ax + B$. Determine the values of $A$ and $B$.